In reversing the direction of drive of servomotors for driving tables, etc. in a machine tool or the like, the machine normally cannot be reversed at once, due to influences of backlash and friction of feed screws. When the quadrant changes while arcuate cutting or the like is being carried out by the machine tool, projections are formed on an arcuate cut surface. In subjecting a workpiece to arcuate cutting on X- and Y-axis planes, for example, the quadrant changes as the machine is driven in the positive direction with respect to the X axis and in the negative direction with respect to the Y axis. When the movement crosses the X axis, for example, the machine is driven in the negative direction with respect to the Y axis without change in direction and in the negative direction with respect to the X axis, switched from the positive direction. In this case, cutting is carried out at the same speed with respect to the Y axis as before the changeover. With respect to the X axis, however, the position deviation becomes "0", so that the torque command value is small, and friction prevents the servomotors from being reversed at once. Moreover, the movement of the tables cannot follow up movement commands and is subject to delay, due to the backlash of the feed screws for feeding the tables. The reduction of the torque command value and the generation of the backlash result in formation of projections on arcuate cut surfaces.
Conventionally, in order to prevent the formation of the projections on the cut surfaces or reduce the height of the projections, a motor control method based on the so-called backlash acceleration correction has been carried out so that the position deviation is subjected to positional backlash correction when the moving direction is reversed. Further a suitable value (acceleration value) is added to a speed command to effect acceleration in the reverse rotating direction of the servomotors, thereby reducing quadrant projections.
FIG. 11 is a block diagram illustrating a motor control method based on backlash acceleration correction (see Jpn. Pat. Appln. KOKAI Publication No. 3-228106, for example) as one method of backlash acceleration. According to this conventional motor control method based on backlash acceleration correction, backlash acceleration correction is effected in a manner such that the value in a speed control loop integrator (term of K1/S in FIG. 11) just before the reversal of direction is obtained, and a value obtained by inverting the sign of this value is used as a target value after the reversal. Further, the backlash acceleration correction is effected in such a manner that and in each speed control loop process within a set time after the reversal of direction, the product of a suitable constant value and a value obtained by subtracting the value in the integrator for each speed control loop process from the target value is used as a backlash acceleration value for each speed control loop process.
However, the conventional motor control method described above has a problem that satisfactory backlash acceleration correction cannot be achieved when the speed of arcuate motion increases.
Referring to FIGS. 12A-12H, the reason for this circumstance will be described. Ideally, the value in the speed control loop integrator should be equal to the sum of frictional torque and acceleration torque components. As the motor rotation is reversed, the sign of the frictional torque is inverted, as indicated by ft1 in FIG. 12C and ft2 in FIG. 12G. On the other hand, the acceleration torque component forms a cosine wave which is obtained by differentiating a speed sine wave with time, and its absolute value has a maximum at the point of time of the reversal of motor rotation, as indicated by al in FIG. 12B and a2 in FIG. 12F.
First, I1 (=a1+ft1) in FIG. 12D represents an ideal behavior of the integrator in the case where the motor rotating speed for arcuate motion is low. Hereupon, according to the conventional motor control method, the target value of the integral value just after the reversal of motor rotation is obtained by multiplying the integrator value just before the reversal by minus 1, so that the acceleration torque component al, as well as the frictional torque component ft1, is inverted. Thus, the conventional target value for the integrator just after the reversal of motor rotation is set at a value which is lower than an ideal target value (value I1 in (d) of FIG. 12 for the time of the reversal of motor rotation) by the acceleration torque component a1.
In the case where the motor speed is thus low, however, the absolute value of the acceleration torque component al is much smaller than that of the frictional torque component ft1 (or is a negligible value), as seen from FIG. 12B and FIG. 12C, so that the conventional target value for the integrator just after the reversal of motor rotation has no specially great difference from the ideal target value mentioned here. Accordingly, the backlash acceleration correction based on the conventional motor control method would arouse no special problem.
When the motor is rotated at high speed, however, the absolute value of the acceleration torque component a2 becomes greater than that of the frictional torque component ft2 by a nonnegligible margin, so that the conventional target value for the integrator just after the reversal is subject to a substantial difference from the ideal target value, i.e., I2 (=a2+ft2) shown in FIG. 12H. Thus, with the backlash acceleration correction based on the conventional motor control method, the target value is set to be so small that satisfactory backlash acceleration correction cannot be effected.
FIG. 13 illustrates how the delay of the reversal can be reduced as indicated by a full line, in contrast with the case where backlash acceleration control is not effected, when the backlash acceleration control is carried out with the acceleration component regarded as negligible and with the aforesaid frictional torque component set so as to be the inverted target value for the speed control loop integrator, in the case where the motor rotating speed for arcuate motion is low.
FIG. 14 illustrates how the inverted target value for the speed control loop integrator becomes lower than a true inverted target value, which contains the acceleration torque component, so that acceleration is not good enough for correct backlash acceleration when the backlash acceleration control is carried out with the acceleration component neglected and with only the frictional torque component set so as to be the inverted target value, in the case where the motor rotating speed for arcuate motion is high.
Thus, the conventional motor control method described above has a problem that satisfactory backlash acceleration correction cannot be achieved if the speed of arcuate motion increases.